In a randomized controlled trial, insecticide-treated bednets were tested as a w

Question

In a randomized controlled trial, insecticide-treated bednets were tested as a way to reduce malaria. Among 346 infants using bednets, 13 developed malaria. Among 271 infants not using bednets, 23 developed malaria. Use a 0.05 significance level to test the claim that the incidence of malaria is lower for infants using bednets. Do the bednets appear to be effective? Conduct the hypothesis test by using the results from the given display. Difference = p(1)-p(2) Eslimate for difference: -0.0472986 95% Test for difference-0 (vs «o): Z =-2.49 P-Value = 0.006 upper bound for difference:-0.00853750 What are the null and alternative hypotheses? B. Ho:P1=P2 O C. Ho:P1 P2 H1 P1P2 Hy P1 P2 H1 P1 P2 ldentify the test statistic. Type an integer or decimal rounded to two decimal places as needed.) ldentify the P-value. (Type an integer or decimal rounded to three decimal places as needed.) What is the conclusion for this test? The P-value is effective. V the significance level a, so Vthe null hypothesis. There is V evidence to support the claim that the incidence of malaria is lower for infants using bednets. The bednets to be

Explanation / Answer

Hypothesis:
H0 : p1 = p2
Ha : p1 < p2

Test statisyics:

p1 = 13/346 = 0.038, n1 = 346
p2 = 23/271 = 0.085 , n2 = 271

p = ( 13+ 23) /( 346 + 271) = 0.0583

z = ( p1 -p2) /sqrt(p *(1-p) *(1/n1+1/n2))
= ( 0.038 - 0.085) / sqrt( 0.0583 *(1-0.0583) *(1/346 + 1/271))
= -2.4876

z =-2.4876

P value = 0.006

The p value is less than the significance level so rejectthe null hypothesis
There is sufficient evidence to support the claim

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